Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?

It's a Tie

Stage: 2 Challenge Level:

Kaia's father always wore a white shirt and coloured tie for work.
He didn't like deciding which tie to wear so he would put his hand
in the drawer and wear the first tie that he pulled out. Each
evening the tie would go back in the drawer.

One Friday morning, Kaia said, "Do you like that tie? You usually
wear it at least twice a week."
"I do not," replied her father, "I have eight ties and I only work
five days a week. I certainly don't wear any tie more than once a
week."
"You have worn that tie twice a week in at least five of the ten
weeks you have been taking me to school," Kaia insisted.
"Impossible! Prove it!" challenged her father.

Do you think Kaia or her father was right? Why?

That weekend Kaia did an experiment. She made the following
drawings of his ties and created the chart shown below.

Week no.

Monday

Tuesday

Wednesday

Thursday

Friday

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

How might Kaia use the drawings and chart to prove her father
wrong?
Try doing an experiment yourself to find out which ties might be
chosen.
What did the result of your experiment show?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.